Use baking soda. Make a paste with baking soda and water. Apply it to the dirty grout using an old toothbrush. Scrub the paste into the grout well. Wash the grout with warm water when you are finished. For the tougher stains, allow the paste to sit for a few minutes before you start scrubbing. One of the most important things in knowing how to clean tile floors is keeping the grout clean. Dirty grout equals dingy-looking floors. Grout is porous and easily .